DALLAS — American Airlines and its parent company filed for bankruptcy protection as they try to cut costs and unload massive debt built up by years of high fuel prices and labor struggles. There will be no impact on travelers for now.

The nation’s third-largest airline also said Tuesday that CEO Gerard Arpey stepped down and was replaced by company president Thomas W. Horton.

AMR Corp. has continued to lose money while other U.S. airlines returned to profitability in the last two years.

Horton said the board of directors unanimously decided to file for bankruptcy after meeting Monday in New York and again by conference call on Monday night.

American said it would operate normally while it reorganizes in bankruptcy. The airline said it would continue to operate flights, honor tickets and take reservations. It said the AAdvantage frequent-flier program would not be affected.